Oscillation Criteria for the Solutions of Higher Order Functional Dierence Equations of Neutral type

In this paper, necessary and sufficient conditions are obtained so that the neutral functionaldifference equation∆m(yn−yτ(n))+qnG(yσ(n)) =fn, n≥n0,admits a positive bounded solution, wherem≥1 is an odd integer, ∆ is the forward differenceoperator given by ∆yn=yn+1−yn;{fn},{qn}, are sequences of real numbers withqn≥0,G∈C(R,R).The results of this paper improve and extend some recent work [6, 15].